In this paper, based on the sample model and data structure technique, we present a quantum-inspired classical randomized fast approximation algorithm, which dramatically reduces the running time to compute statistical leverage scores of low-rank matrix. It is a generalization of method in [1]}, [2]}, the core ideas of our implementations of algorithm REF  is FKV algorithm [2]}, but with different parameter setting for choosing the sampling matrix size. It can improve the error of low rank matrix approximation, then we use algorithm REF  to approximate the statistic leverage scores, which combines with inner product estimation method in [1]}. Next, we theoretically analyze the approximation accuracy and the time complexity of our algorithm. When the matrix size is large, the time complexity of previous work on computing the statistical leverages scores is at least linear in matrix size, our algorithm takes time polynomial in integer \(k\) , condition number \(\kappa \)  and logarithm of the matrix size, and we achieve an exponential speedup when the rank of the input matrix is low-rank. Our numerical experiments show that the QiSLS algorithm performs well in practice on large datasets.
